UNIFIED INTERVAL ESTIMATION FOR RANDOM COEFFICIENT AUTOREGRESSIVE MODELS

The consistency of the quasi-maximum likelihood estimator for random coefficient autoregressive models requires that the coefficient be a non-degenerate random variable. In this article, we propose empirical likelihood methods based on weighted-score equations to construct a confidence interval for the coefficient. We do not need to distinguish whether the coefficient is random or deterministic and whether the process is stationary or non-stationary, and we present two classes of equations depending on whether a constant trend is included in the model. A simulation study confirms the good finite-sample behaviour of our resulting empirical likelihood-based confidence intervals. We also apply our methods to study US macroeconomic data.